Answer:
a) 0.2503 = 25.03% probability that exactly 3 have green seeds.
b) 0.4744 = 47.44% probability that more than 2 have green seeds.
c) 0.1020 = 10.20% probability that more than 30 have green seeds.
d) 0.1414 = 14.14% probability that between 30 and 35 inclusive have green seeds.
e) 0.8508 = 85.05% probability that fewer than 80 have yellow seeds
Step-by-step explanation:
For questions a and b, the binomial probability distribution is used. For questions c, d and e, the binomial distribution is approximated to the normal.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
A) Out of 10 offspring of heterozygous plants, what is the probability that exactly 3 have green seeds?
10 offspring of heterozygous plants means that [tex]n = 3[/tex]
Probability 0.25 of having green seeds means that [tex]p = 0.25[/tex]
This probability is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{10,3}.(0.25)^{3}.(0.75)^{7} = 0.2503[/tex]
0.2503 = 25.03% probability that exactly 3 have green seeds.
B) Out of 10 offspring of heterozygous plants, what is the probability that more than 2 have green seeds?
This is
[tex]P(X > 2) = 1 - P(X \leq 2)[/tex]
In which
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.25)^{0}.(0.75)^{10} = 0.0563[/tex]
[tex]P(X = 1) = C_{10,1}.(0.25)^{1}.(0.75)^{9} = 0.1877[/tex]
[tex]P(X = 2) = C_{10,2}.(0.25)^{2}.(0.75)^{8} = 0.2816[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0563 + 0.1877 + 0.2816 = 0.5256[/tex]
[tex]P(X > 2) = 1 - P(X \leq 2) = 1 - 0.5256 = 0.4744[/tex]
0.4744 = 47.44% probability that more than 2 have green seeds.
C) Out of 100 offspring of heterozygous plants, what is the probability that more than 30 have green seeds?
Now
[tex]n = 100[/tex]
[tex]\mu = E(x) = np = 100*0.25 = 25[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.25*0.75} = 4.33[/tex]
Using continuity correction, this is [tex]P(X > 30 + 0.5) = P(X > 30.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 30.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30.5 - 25}{4.33}[/tex]
[tex]Z = 1.27[/tex]
[tex]Z = 1.27[/tex] has a pvalue of 0.8980
1 - 0.8980 = 0.1020
0.1020 = 10.20% probability that more than 30 have green seeds.
D) Out of 100 offspring of heterozygous plants, what is the probability that between 30 and 35 inclusive have green seeds?
Using continuity correction, this is [tex]P(30-0.5 \leq X \leq 35 + 0.5) = P(29.5 \leq X \leq 35.5)[/tex], which is the pvalue of Z when X = 35.5 subtracted by the pvalue of Z when X = 29.5.
X = 35.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35.5 - 25}{4.33}[/tex]
[tex]Z = 2.42[/tex]
[tex]Z = 2.42[/tex] has a pvalue of 0.9922
X = 29.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{29.5 - 25}{4.33}[/tex]
[tex]Z = 1.04[/tex]
[tex]Z = 1.04[/tex] has a pvalue of 0.8508
0.9922 - 0.8508 = 0.1414
0.1414 = 14.14% probability that between 30 and 35 inclusive have green seeds.
E) Out of 100 offspring of heterozygous plants, what is the probability that fewer than 80 have yellow seeds?
0.75 probability of yellow seeds, so [tex]p = 0.75[/tex]. So
[tex]\mu = E(x) = np = 100*0.75 = 75[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.75*0.25} = 4.33[/tex]
This probability is [tex]P(X < 80 - 0.5) = P(X < 79.5)[/tex], which is the pvalue of Z when X = 79.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{79.5 - 75}{4.33}[/tex]
[tex]Z = 1.04[/tex]
[tex]Z = 1.04[/tex] has a pvalue of 0.8508
0.8508 = 85.05% probability that fewer than 80 have yellow seeds
Can someone help me with this plz??
Answer:
f(-3) = -2(-3)^3 - 3
f(-3) = 54 - 3
f(-3) = 51
g(3) = -5(3) + 4
g(3) = -15+4
g(3) = -11
Hope this helps!
Like the land bridge people, what factors might have pulled the Solutreans into North America?
overpopulation
job opportunities
better schools
grasses and animals
Answer:
mayne because of grasses and animals
Answer:
D
Step-by-step explanation:
2.
(02.05 MC)
Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(3, −6), Q(0, 9), and R(−3, 0). Triangle P′Q′R′ has vertices P′(1, −2), Q′(0, 3), and R′(−1, 0).
Plot triangles PQR and P′Q′R′ on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)
Answer:
P' = 1/3 P
reflection in the y-axis just changes the sign of all the x-values.
Since P" ≅ P', and P' is smaller than P, P" cannot be ≅ to P
It is, however, similar to P.
Answer:
P' = 1/3 P
Step-by-step explanation:
Reflection in the y-axis just changes the sign of all the x-values. Since P" ≅ P', and P' is smaller than P, P" cannot be ≅ to P . It is, however, similar to P.
Good luck!!
Factor the expression. Rewrite the
expression by factoring the Greatest
Common Factor GCF.
32xy + 24x
GCF
Answer:
8x(4y+3)
Step-by-step explanation:
32xy+24x
GCF is 8x, so factor that out
8x(4y+3)
distribute to check,
32xy+24x
"Two planes leave the airport at the same time. Plane 1 travels just 9 miles east from
the airport while Plane 2 travels 40 miles north from the airport. What is the diagonal
distance from plane 1 and 2?"
n = 40, p=0.95, X = 38
P(38) =
Answer:
36.1
Step-by-step explanation:
Work out the area of a rectangle with base, b = 20mm and perimeter, P = 60mm.
b
The diagram is not drawn to scale.
base+perimeter
20mm+60mm
=80mm
Where should you place parentheses in the expression 2 + 6 ÷ 2 + 4 × 3 so that the value of the expression is 16? Multiple choice question
Answer: (2+6)÷ 2 + 4 × 3
Answer:
4x3
Step-by-step explanation:
What is the value of ?
18 - (2 x ? ) = ? x 4
Answer:
?= 3
Step-by-step explanation:
let x = ？
18-2x=4x
6x=18x
x=3
Answer:
The value of ? is 3
Step-by-step explanation
Lets call ? x
18-2x = 4x
18=6x
3=x
Look at screen shoottttttttttttttttttttttttttttttttttt
Olivia baked 21 mini-loaves of banana bread to be sliced for snacks at a craft fair. She will place an equal number of loaves in 4 different locations.
How many loaves will be at each location?
Divide to find the quotient and remainder.
r
4 parenrightzb 21
Decide how to use the quotient and remainder to answer the question.
There will be loaves at each location.
What is the slope between the points (2,5) and (6,13)
Let me = slope
m = (13 - 5)/(6 - 2)
m = 8/4
m = 2
The slope is 2.
Solve | 2x - 6 | = |x| by graphing
Answer:
X=2 & X=6
Step-by-step explanation:
If you graph the equation (I recommend using desmos) you can see that X equals 2 & 6.
figure above shows a bkock of isometric projection draw the 1st angle projection taking F a as a font elevation
117AUG 2017
Answer:
ufhvuaejahejgjbhrthugjwergkwer
Step-by-step explanation:
erlgluerhbferihgqerhggyefuqwheuhqhwgh4ht43y3yhebr
Helpppp!!!
Which equation can be used to find the length -of AC?
What fractions will make the comparison true? 5/8>
Answer:
7/10
Step-by-step explanation:
i7/10 is greater than 5/8
Given p || q and ∠4 = 130°, find the measure of angles 1, 2, 3, 5, 6, 7, and 8. Label on the diagram.
I NEED HELP ASAP
Simplify the expression (8n^4-6n+8n^2)+(6n^4-4)
Answer:
(8n^4-6n+8n^2)+(6n^4-4)
8n^4 + 8n^2 - 6n + 6n^4 - 4
14n^4 + 8n^2 - 6n - 4
Step-by-step explanation:
Help fast help fast help Help fast help fast help Help fast help fast help Help fast help fast help Help fast help fast help Help fast help fast help Help fast help fast help Help fast help fast help Help fast help fast help Help fast help fast help
Answer: its 3x+20 to my calculations
Step-by-step explanation:
Yes or No: Is this triangle a Right Triangle with side measures 21, 28, 352
La densidad del agua es 1g/cc determinar su equivalente en libras/pie3 y en kg/m3
Answer:
Las equivalencias de la densidad del agua son: Densidad kg/m3 = 1000 kg/m3. y Densidad lb/pie3 = 0.016 lb/pie3. Explicación paso a paso: La densidad del agua es de 1g/cc = 1 g/cm3.
On a BWIA flight, 2/3 of the
passengers are from Trinidad.
If there are 189 passengers
altogether, how many were
from Trinidad?
Answer:
126 passengers from Trinidad.
Step-by-step explanation:
Given that,
On a BWIA flight, 2/3 of the passengers are from Trinidad.
Total passengers = 189
We need to find how many were from Trinidad. It can be calculated by finding 2/3 of 189 such that,
[tex]P=\dfrac{2}{3}\times 189\\\\=126[/tex]
Hence, there were 126 passengers from Trinidad.
Tomás is gathering data about the sleeping habits of high school students. So far, he has completed 3 different surveys, each with 70 respondents.
What should Tomás expect as he continues his data-gathering process?
As the number of surveys increases, the mean of the sample means will approach ______, and the means will be ___________.
70 Points
Answer:
The population mean
Normally distributed
Please give me brainliest, I really need it.
a)As the number of surveys increases, the mean of the sample means will approach the population mean.
b)Means will be normally distributed.
What is a normal distribution?A normal distribution is a probability distribution that is symmetric about the mean, and data near the mean are more frequent than data far from the mean.
As the number of surveys increases, we will have more data.
So, the mean of the sample means will approach the population mean.
Means will be normally distributed because each survey has the same number of respondents.
Thus, a)as the number of surveys increases, the mean of the sample means will approach the population mean.
b)Means will be normally distributed.
To get more about normal distribution visit:
https://brainly.com/question/4079902
I need help with this
Answer:
The length of AB is 18
Step-by-step explanation:
Do the pygotham theorem
24^2 + 7^2 = 625
Square root the answer
[tex]\sqrt{625}[/tex] = 25
Line BO equals 7 because CO is 7 and they are both radiuses
Subtract the answer to the length BO
25 - 7 = 18
18 is the length of AB bro
F(x,y)=-2x^2-2xy-2y^2+35x+42y-158
Answer:
x^3 + x^2 + 2x^2y + xy^2 + y^2 + 2xy
Step-by-step explanation:
ihope makaktulong
if wrong correct me
Evaluate :
32¯2/5 how do i evaluate this? With the minus.
Answer:
I'm sorry I don't know the answer. But have you tried Photomath? it helps me so much! have a good day/night! ❤️
Find the logarithm of 2025 to the base 3√5
Answer:
3.99 ≈ 4
Step-by-step explanation:
I wish this is correct
Is the value 5 a solution to the inequality r + 4 < 7 ?
UHM- I NEED HELP AGAIN- YOU"LL GET 100 POINTS! <3
Answer:
no
Step-by-step explanation:
5+4=9 which is greater than 7
Answer:
No, i don't think so
Step-by-step explanation:
.On 1st March 2001, the ratio of Freddie’s age to his mother’s age was 1:11
On 1st March 2018, the ratio of Freddie’s age to his mother’s age was 2:5
Write the ratio of Freddie’s age to his mother’s age on 1st March 2030
Answer:
[tex]Ratio =16 : 31[/tex]
Step-by-step explanation:
Let
x = Freddie's age and y = His mother's age
Given
2001:= [tex]x : y = 1 : 11[/tex]
2018:= [tex]x +17: y + 17= 2 : 5[/tex]
Required
The ratio of their age in 2030
[tex]x : y = 1 : 11[/tex]
[tex]x +17: y + 17= 2 : 5[/tex]
Express as fractions
[tex]\frac{x}{y} = \frac{1}{11}[/tex] --- (1)
[tex]\frac{x+17}{y+17} = \frac{2}{5}[/tex] -- (2)
In (1), make y the subject
[tex]\frac{x}{y} = \frac{1}{11}[/tex]
[tex]y = 11x[/tex]
Substitute [tex]y = 11x[/tex] in (2)
[tex]\frac{x+17}{y+17} = \frac{2}{5}[/tex]
[tex]\frac{x+17}{11x+17} = \frac{2}{5}[/tex]
Cross Multiply
[tex]5(x +17) = 2(11x + 17)[/tex]
[tex]5x +85 = 22x + 34[/tex]
Collect like terms
[tex]22x - 5x = 85 - 34[/tex]
[tex]17x = 51[/tex]
[tex]x =3[/tex]
[tex]y = 11x[/tex]
[tex]y = 11*3[/tex]
[tex]y = 33[/tex]
This means that: In 2001, Freddie was 3 and his mother was 33
In 2030 (29 years after);
Freddie will be: 3 + 29 = 32
His mother will be: 33 + 29 = 62
So, the ratio is:
[tex]Ratio =32 : 62[/tex]
Divide by 2
[tex]Ratio =16 : 31[/tex]
is (x-4) a factor of 2x^4-9x^3-20x^2+147x-180? find out by using the factor theorem.
Answer: (x-4) is not a factor of the given polynomial.
===================================================
Explanation:
Rule: If (x-k) is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem. We can take this in reverse to say that if p(k) = 0, then (x-k) must be a factor of p(x).
In this case, we have k = 4 and we can find that:
p(x) = 2x^4-9x^3-20x^2+147x-180
p(4) = 2(4)^4-9(4)^3-20(4)^2+147(4)-180
p(4) = 24
The result we get is not zero, so that means (x-4) is not a factor of p(x).